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BIFURCATIONS OF PERIODIC ORBITS IN THREE-WELL DUFFING SYSTEM WITH A PHASE SHIFT

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Journal of Systems science & Complexity 2011年第3期24卷 519-531页

作者： Jicai HUANG Han ZHANG School of mathematics and Statistics Central China Normal University Wuhan 430079 China college of information Technical science Nankai University Tianjin 300071 China.

Bifurcations of periodic orbits of three-well Duffing system with a phase shift are investigated in detail. The conditions of the existence and bifurcations for harmonics, subharmonics （2-order, 3- order and m-order） and superharmonics under small perturbations are given by using second-order averaging method and Melnikov＇s method. The influence of the phase shift on the dynamics is also obtained.

关键词： Bifurcations Melnikov's method periodic orbits second-order averaging three-well Duffing system.

Universal approximation of polygonal fuzzy neural networks in sense of K-integral norms

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science china(information sciences) 2011年第11期54卷 2307-2323页

作者： WANG GuiJun 1 & LI XiaoPing 2 1 School of mathematics science,Tianjin normal university,Tianjin 300387,china 2 School of Management,Tianjin normal university,Tianjin 300387,china 1. School of mathematics science Tianjin Normal University Tianjin 300387 China2. School of Management Tianjin Normal University Tianjin 300387 China

In this paper,we introduce polygonal fuzzy numbers to overcome the operational complexity of ordinary fuzzy numbers,and obtain two important inequalities by taking advantage of their fine *** presenting an actual example,we demonstrate that the approximation capability of polygonal fuzzy numbers is ***,the concepts of K-quasi-additive integrals and K-integral norms are *** the polygonal fuzzy numbers space satisfies separability,the density problems for several functions spaces can be studied,by means of fuzzy-valued simple functions and fuzzy-valued Bernstein *** establish that the class of the integrally-bounded fuzzy-valued functions spans a complete and separable metric space in the K-integral ***,in the sense of K-integral norms,the universal approximation of fourlayer regular polygonal fuzzy neural networks for fuzzy-valued simple functions is ***,we show that this type of networks also possesses universal approximation for the class of integrally-bounded fuzzyvalued *** result indicates that the approximation capability which regular polygonal fuzzy neural networks for continuous fuzzy systems can be extended as for general integrable systems.

关键词： polygonal fuzzy numbers K-quasi-additive integrals K-integral norms polygonal fuzzy neural networks universal approximations

Cluster based node scheduling method for wireless sensor networks

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science china(information sciences) 2012年第4期55卷 755-764页

作者： WANG Lei 1,2,WEI RuiZhong 2 & TIAN ZiHong 2,3 1 college of Software,Hunan university,Changsha 410082,china 2 Department of Computer science,Lakehead university,Thunder Bay P7B 5E1,Canada 3 mathematics and information science college,Hebei normal university,Shijiazhuang 050016,china 1. college of Software Hunan University Changsha 410082 China2. Department of Computer Science Lakehead University Thunder Bay P7B 5E1 Canada3. Mathematics and Information Science College Hebei Normal University Shijiazhuang 050016 China

By researching on the node scheduling problem of m-covered and connected sensor networks,a new concept of two-hops-cluster is proposed in this paper,and based on it,a new distributed node scheduling algorithm THCNS for allocating all nodes in the sensor network into k(k≤m) different groups {0,1,...,k 1} is designed,without requiring location *** algorithm guarantees that each group to be connected and maintains the coverage ratio with high *** analysis and simulation results show that it has better performance than previous randomized scheduling scheme,and can prolong the lifetime of the sensor network effectively.

关键词： node scheduling lifetime wireless sensor network two-hops-cluster

Homotopy type of smooth weighted complete intersections

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science china mathematics 2010年第6期53卷 1583-1594页

作者： WANG JianBo1,& WANG YuYu2 1Department of mathematics,Tianjin university,Tianjin 300072,china 2college of Mathematical science,Tianjin normal university,Tianjin 300387,china 1. Department of mathematics Tianjin University Tianjin 300072 China2. College of Mathematical Science Tianjin Normal University Tianjin 300387 China

If the total degree d has no prime divisors less than(n+3)/2,then we prove that the homotopy type of complex odd dimensional smooth weighted complete intersection Xn(d;w) is determined by the dimension n,the total degree d,the Euler characteristic and the Kervaire invariant,provided that the weights w =(ω0,...,ωn+r) is pairwise relatively prime.

关键词： weighted projective space weighted complete intersection homotopy type connected sum

Weighted weak type estimates for commutators of the Marcinkiewicz integrals

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science china mathematics 2004年第1期47卷 83-95页

作者： DING Yong, LU Shanzhen & ZHANG PuDepartment of mathematics, Beijing normal university, Beijing 100875, china Department of information and Computing science, Zhejiang Institute of science and Technology, Hangzhou 310033, china 1. Department of mathematics Beijing Normal University 100875 Beijing China 2. Department of information and Computing science Zhejiang Institute of Science and Technology 310033 Hangzhou China

In this paper the authors give the weighted weak LlogL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities... 详细信息

关键词： Marcinkiewicz integral, commutator, Ap weight, weak type estimate.

Multiwavelet sampling theorem in Sobolev spaces

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science china mathematics 2010年第12期53卷 3197-3214页

作者： LI YouFa 1,2 & YANG ShouZhi 1, 1 Department of mathematics, Shantou university, Shantou 515063, china 2 college of mathematics and information sciences, Guangxi university, Nanning 530004, china 1. Department of mathematics Shantou University Shantou 515063 China2. College of Mathematics and Information Sciences Guangxi University Nanning 530004 China

This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.

关键词： Sobolev spaces refinable function vectors dual multiwavelet frames delta function sampling theorem

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

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science china mathematics 2011年第3期54卷 587-602页

作者： HU GuoEn1 & LU ShanZhen2 1Department of Applied mathematics, Zhengzhou information science and Technology Institute, Zhengzhou 450002, china 2Department of mathematics, Beijing normal university, Beijing 100875, china 1. Department of Applied mathematics Zhengzhou Information Science and Technology Institute Zhengzhou 450002 China2. Department of Mathematics Beijing Normal University Beijing 100875 China

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot... 详细信息

关键词： approximation to the identity weighted norm inequality singular integral operator non-smooth kernel Calderón-Zygmund decomposition

Quantum nonlocality of generic family of four-qubit entangled pure states

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Chinese Physics B 2015年第7期24卷 83-87页

作者：丁东何英秋闫凤利高亭 college of Physics science and information Engineering Hebei Normal University Department of Basic Curriculum North China Institute of Science and Technology college of mathematics and information science Hebei Normal University

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states ｜Gabcd〉[Phys. Rev. A 65 052112（2002）] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called ＂four-qubit the maximally entangled state ｜Gm〉＂ and it is also violated by four-qubit W state and a special family of states ｜Gab00〉. Moreover, a useful entanglement-nonlocality relationship for the family of states ｜Gab00〉is derived. Finally, we present a scheme of preparation of the state ｜Gm〉with linear optics and cross-Kerr nonlinearities.

关键词： quantum nonlocality Bell-type inequality quantum entanglement

Identification of Semen Celosiae and Cockscomb Flower Using Continuous Wavelet Transform with FTIR

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稀有金属材料与工程 2006年第S3期 614-616页

作者： Changjiang Zhang~1 Cungui Cheng~2 (1.college of mathematics,Physics and information Engineering,Zhejiang normal university,Jinhua 321004,china) (2.college of Chemistry and Life science,Zhejiang normal university,Jinhua 321004,china)

Infrared spectra of semen celosiae and cockscomb flower can be obtained directly,quickly and accurately employing Fourier transform infrared spectroscopy (FTIR) with OMN1 *** wavelet transform (CWT) is employed to zoom in local region of infrared spectra of semen celosiae and cockscomb *** difference of infrared spectra between semen celosiae and cockscomb flower is greatly *** rate is greatly improved. Daubechies wavelet is used as mother *** is implemented to the infrared spectra of semen celosiae and cockscomb *** difference between semen celosiae and cockscomb flower is observed at all scales in the continuous wavelet *** optimal scale is selected to identify semen celosiae and cockscomb *** results show that it is effective to apply CWT on the basis of FTIR to identify traditional Chinese medicinal materials,which are the same general but different species.

关键词： semen celosiate cockscomb flower FTIR CWT Chinese medical material